# Variance vs. Standard Deviation — What's the Difference?

By Tayyaba Rehman — Published on November 26, 2023
Variance measures how data spreads from the mean; standard deviation is the square root of variance, indicating average deviation from the mean.

## Key Differences

Variance is a statistical term that quantifies how much individual numbers in a dataset deviate from the mean of the dataset. It essentially provides a measure of the spread or dispersion of the data points. By calculating variance, one can get a sense of how much variability or inconsistency exists within a set of observations.
Standard deviation, on the other hand, is a measure that expresses the average amount each number in a dataset differs from the mean. It's calculated by taking the square root of the variance. Standard deviation gives a more intuitive sense of the spread because its unit is the same as the original data, making it easier to interpret in many practical scenarios.
Variance and standard deviation are both crucial concepts in statistics and data analysis. Variance helps in understanding the distribution and magnitude of the spread, while standard deviation gives a direct understanding of the average dispersion from the mean.
In many applications, standard deviation is preferred over variance because of its interpretability. While variance gives a squared measure of dispersion, standard deviation provides an absolute measure, directly comparable to the original data points.
When dealing with data, understanding variance and standard deviation is essential. Variance informs about the total spread, while standard deviation shows the average distance of data points from the mean.

## Comparison Chart

### Definition

Measure of data's dispersion from mean.
Square root of variance; average deviation from the mean.

### Unit

Squared units of the original data.
Same units as the original data.

### Interpretability

Less direct; squared measure.
More intuitive; average distance from mean.

### Formula Component

Sum of squared deviations divided by the number of data points.
Square root of variance.

## Compare with Definitions

#### Variance

Measure of how data points differ from the dataset's mean.
The variance of the test scores was quite high, indicating diverse performance.

#### Standard Deviation

Indicator of average spread from the average value.
A low standard deviation in the factory's output indicated consistent production.

#### Variance

Represents squared deviation of a variable's values.
By studying the variance, researchers could gauge the reliability of the experiment.

#### Standard Deviation

Average distance data points deviate from the mean.
The standard deviation of the dataset revealed significant inconsistencies.

#### Variance

Indicator of data's spread or dispersion.
A higher variance in the sales data meant more unpredictable sales patterns.

#### Standard Deviation

Statistical tool to gauge average variability.
Standard deviation provided a clearer picture of the patient's varying heart rates.

#### Variance

Statistical tool to quantify variability.
To understand the fluctuation in monthly expenses, she calculated the variance.

#### Standard Deviation

Measure of data's dispersion in original units.
High standard deviation in grades pointed to varied student performance.

#### Variance

The state or quality of being variant or variable; variation
Considerable variance in temperature across the region.

#### Standard Deviation

Square root of the variance.
To find the standard deviation, he first calculated the variance and then its square root.

#### Variance

Difference or inconsistency

#### Variance

The state or fact of being in disagreement or in conflict
I am at variance with her over who should pay for the damage.

#### Variance

A discrepancy between two statements or documents, especially between the charge in a criminal indictment and the evidence presented.

#### Variance

An exception to the application of a usual rule, granted by an authority on the basis of hardship or practicality
A zoning variance.

#### Variance

(Statistics) The square of the standard deviation.

#### Variance

(Chemistry) The number of thermodynamic variables, such as temperature and pressure, required to specify a state of equilibrium of a system, given by the phase rule; the degrees of freedom of a system.

#### Variance

The act of varying or the state of being variable.

#### Variance

A difference between what is expected and what is observed; deviation.

#### Variance

The state of differing or being in conflict.

#### Variance

An official permit to do something that is ordinarily forbidden by regulations.

#### Variance

(law) A discrepancy between two legal documents.

#### Variance

(law) A departure from a cause of action originally in a complaint.

#### Variance

(statistics) The second central moment in probability.

#### Variance

The number of degrees of freedom in a system.

#### Variance

Covariance and contravariance generally.
Depending on the variance of the type constructor, the subtyping relation of the simple types may be either preserved, reversed, or ignored for the respective complex types.

#### Variance

The quality or state of being variant; change of condition; variation.

#### Variance

Difference that produces dispute or controversy; disagreement; dissension; discord; dispute; quarrel.
That which is the strength of their amity shall prove the immediate author of their variance.

#### Variance

A disagreement or difference between two parts of the same legal proceeding, which, to be effectual, ought to agree, - as between the writ and the declaration, or between the allegation and the proof.

#### Variance

The expected value of the square of the deviation from the mean of a randomly distributed variable; the second moment about the mean. This is also the square of the standard deviation.

#### Variance

An event that departs from expectations

#### Variance

Discord that splits a group

#### Variance

The second moment around the mean; the expected value of the square of the deviations of a random variable from its mean value

#### Variance

A difference between conflicting facts or claims or opinions;
A growing divergence of opinion

#### Variance

The quality of being subject to variation

#### Variance

An activity that varies from a norm or standard;
Any variation in his routine was immediately reported

#### Variance

Average of squared differences from the mean.
With such a low variance, the team's consistency was evident.

## Common Curiosities

#### How is standard deviation related to variance?

Standard deviation is the square root of variance.

#### What is variance?

Variance is a measure of how data points differ from the dataset's mean.

#### What does a low standard deviation indicate?

It indicates data points are closer to the mean, showing less variability.

#### How do outliers affect variance and standard deviation?

Outliers can significantly increase both variance and standard deviation.

#### Why might someone use variance over standard deviation?

Variance can be useful in mathematical computations and modeling.

#### Which one is more interpretable, variance or standard deviation?

Standard deviation, as it's in the original units of data.

#### Can standard deviation be negative?

No, since it's derived from the square root of variance, it's always non-negative.

#### Does higher variance always mean higher standard deviation?

Yes, since standard deviation is derived from variance.

#### Why is variance squared?

Squaring ensures all differences are positive, providing a clear measure of spread.

#### Can variance give an idea about the shape of data distribution?

Not entirely. While it shows spread, it doesn't specify distribution shape like skewness.

#### Why is standard deviation a popular measure in finance?

It provides a clear indication of investment risk, with higher values indicating more unpredictability.

#### Is variance the average of squared deviations?

Yes, it's the mean of the squared differences from the mean.

#### In which scenarios might standard deviation be more useful than variance?

When comparing the spread of two datasets or interpreting spread in the original data's context.

#### Does a standard deviation of zero mean no variance?

Yes, a standard deviation of zero also means the variance is zero.

#### Do variance and standard deviation measure central tendency?

No, they measure dispersion. Central tendency is measured by means like the mean or median.